Gravitational constant and navigation

This is an offshoot of the Brilliant Light Power thread, from which posts dealing with the gravitational constant G were AAH'd for being off-topic (I think).

michaelsuede said (excerpted):

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Originally Posted by michaelsuede (Post 11661375) Since the ground state is simply defined, there's no reason in theory it could not be lower. It's like big G simply being defined, even though it changes every time we measure it.

I said this was "nonsense", and the conversation went like this:

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Originally Posted by sts60 You're conflating refinement of very well-known empirical constants - which fit theory very, very well - with casual wholesale revisions of same. That is fantasy.

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Originally Posted by michaelsuede OH!! It's "refinement" - that's why the numbers are all over the board.

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Originally Posted by sts60 The notion that G values are "all over the board" is flatly at odds with reality. The current standard measured value of G is about 1% different than that originally measured over two centuries ago. And if G actually varied as much as you portray, we'd never have sent spacecraft to Mars, let alone to Pluto and beyond.

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Originally Posted by michaelsuede NASA navigates the cosmos with purely Newtonian calculations where the variance of G can be great and not make a bit of difference given that most long range probes operate off of celestial navigation. Clearly we could still effectively navigate the solar system even with a very gross definition of G.

I scoffed heartily at this, because (a) michaelsuede doesn't understand how "celestial navigation" works for spacecraft. But more importantly, (b) it's silly to claim that any old value of G ("the variance can be great") can be used and expect that you're going to get where you're going over interplanetary distances.

michealsuede's followup comment in the main thread was:

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Originally Posted by michaelsuede (Post 11662760) I said it was possible to navigate around the solar system using celestial navigation and a gross approximation of G, like the one that was taken by Cavendish back in 1798. I'm still struggling to understand how I'm wrong about this... ...Measurements of G are all over the place. The Scientific American has done several articles and podcasts about this. I made this claim in reference to G not being proven to be a constant, which it is not. It is simply defined, not empirically proven, to be a constant.

So, this thread is for discussion of such issues. The first topic, as I see it, is: What does he mean by "gross approximation" and "all over the place"?

The original determination of the value of G, made by Cavendish in 1798, was about 6.754 ×10^-11 N m²kg^-2.
The current accepted value is about G = 6.673×10^-11 N m²kg^-2.

In other words, the current value is about 1% different than the first value, which is hardly surprising; gravitation is by far the weakest force and this makes a precise determination of G very difficult. And I know he's talking about more than the normal evolution of measurement of a physical constant, but I'd like to make sure we're at the same starting point.

michaelsuede, what do you mean by "the variance of G can be great" in space missions? Are you talking about up to 1%? 5%? 25%? I want to be sure I'm not getting the wrong impression from your adjectives.

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